Several different ways to attack this one. Around here, lightweight has different meanings to different folks. I have an '06 thats around 8lb, that i consider light, but may not be to you if your looking for a 6lb rifle.
I'm sure their have been elk shot with 7mm-08 and .308 (hell, Ive heard of guys using a .243) but my opinion is that with elk on the menu, a long action would be in order. 280, 30-06 into the magnums etc.
Hope this helps. Clear as mud now, right?